Internal problem ID [973]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear
Equations. Section 2.3 Page 60
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 x \left (y-1\right )^{\frac {1}{3}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 9] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 13
dsolve([diff(y(x),x)=3*x*(y(x)-1)^(1/3),y(0) = 9],y(x), singsol=all)
\[ y \relax (x ) = x^{2} \sqrt {x^{2}+4}+4 \sqrt {x^{2}+4}+1 \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 16
DSolve[{y'[x]==3*x*(y[x]-1)^(1/3),y[0]==9},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x^2+4\right )^{3/2}+1 \\ \end{align*}